The position of an object moving along a line is given by #p(t) = 3t - sin(( pi )/6t) #. What is the speed of the object at #t = 2 #?

1 Answer
Aug 30, 2017

Answer:

The speed is #=2.74ms^-1#

Explanation:

The position of the the object is given by the equation

#p(t)=3t-sin(1/6pit)#

The speed is the derivative of the position

#v(t)=(dp)/(dt)=3-1/6picos(1/6pit)#

When #t=2#

#v(t)=3-1/6picos(1/6pi*2)#

#=3-1/6picos(1/3pi)#

#=3-1/6pi*1/2#

#=2.74#